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The first goal of this monograph is to explain the undefined primitive ideas and the axioms which shape the root of Einstein's thought of precise relativity. Minkowski space-time is constructed from a suite of self sustaining axioms, said by way of a unmarried relation of betweenness. it's proven that every one types are isomorphic to the standard coordinate version, and the axioms are constant relative to the reals.

15) prove that, for every positive e, lim(1 — r)2P'M(r, f) = 0. 5 Suppose that f i (z) = f(z) C where C is a constant and that W(R), Wi(R) refer to f(z), f 1 (z) respectively. Prove that W(R —1c1) W1(R) W(R +10). 15) then so does f i (z). 13) without f (z) doing so. 4 Simultaneous growth near different boundary points We have seen that a function f (z) mean p-valent in lz I < 1 satisfies (z)1 = 0(1 — r) -2P (1z1 = r). However a function can be as large as this only on a single rather small arc of Izi = r.

Her method, based on a distortion theorem of Ahlfors [1930], was extended by Spencer [1940b] to the more general case. If f(z) = ao + aiz + ... 3) = v=0 This dependence is essential. In fact any polynomial of degree p is p-valent and has at most p zeros in iz 1 < 1, but bounds for M(r) must clearly depend on all the coefficients. 1 A length-area principle 29 cannot grow too rapidly near several points of lz1 = 1 simultaneously, and in particular that, if M(r) attains the growth (1 — r)-2P, then if (r )1 attains this magnitude for a single fixed value of 0, and is quite small for other constant 0 as r 1.